We propose some questions about Fukaya categories. Given a class of isomorphisms $0 sim tau$, where $tau$ represents the truth value of a particle, and $0$ is a $0$ object in a Fukaya category, what are its spectral homology theories? This is a variation on the works of P. Seidel and E. Riehl.

This paper presents a deep learning-based approach for stock price prediction in financial markets. The problem of accurately predicting future stock price movements is of crucial importance to investors and traders, as it allows them to make informed investment decisions. Deep learning, a branch of artificial intelligence, offers new perspectives for meeting this complex challenge. Deep learning models, such as deep neural networks, are capable of extracting complex features and patterns from large amounts of historical data on stock prices, trading volumes, financial news and data. other relevant factors. Using this data, deep learning and machine learning models can learn to recognize trends, patterns, and non-linear relationships between variables that can influence stock prices. Once trained, these models can be used to predict future stock prices. This study aims to find the most suitable model to predict stock prices using statistical learning with deep learning and machine learning methods RNN, LSTM, GRU, SVM and Linear Regression using the data on Apple stock prices from Yahoo Finance from 2000 to 2024. The result showed that SVMmodeling is not suitable for predicting Apple stock prices. In comparison,GRUshowed the best performance in predicting Apple stock prices with a MAE of 1.64 and an RMSE of 2.14 which exceeded the results of LSTM, Linear regression and SVM. The limitation of this research was that the data type was only time series data. It is important to note, however, that stock price forecasting remains a complex challenge due to the volatile nature of financial markets and the influence of unpredictable factors. Although deep learning models can improve prediction accuracy, it is essential to understand that errors can still occur.

We compute and explore the full geometric product of two oriented points in conformal geometric algebra Cl(4,1) of three-dimensional Euclidean space. We comment on the symmetry of the various components, and state for all expressions also a representation in terms of point pair center and radius vectors.

Suppose that $y>0$, $0leqalpha<2pi$ and $0<K<1$. Let $P^+$ be the set of primes $p$ such that $cos(yln p+alpha)>K$ and $P^-$ the set of primes $p$ such that $cos(yln p+alpha)<-K$ . In this paper we prove $sum_{pin P^+}frac{1}{p}=infty$ and $sum_{pin P^-}frac{1}{p}=infty$.

A recent investigation by the author revealed the proton-electron mass ratio, a dimensionless number, could be approximates extremely well by a simple closed form equation, namely the fourth root of an integer. The result inspired the reader to account for the fact. This paper details some preliminary theorizing that partly explains the fact. Why the integer has the value that it does remains an open question.

This document is devoted to understanding and implementing the energy numbers, which were recently explicated very clearly by Emmerson in his recent paper. Through this line of reasoning, it becomes apparent that the algebra defined by the energy numbers are indeed the natural algebra for categorifying quantization. We also develop a notion of symmetric topological vector spaces, and forcing on said spaces motivated by homological mirror symmetry.

In this paper we enumerate the fine structure constant, the proton-electron mass ratio, the neutron-electron mass ratio and the neutron-proton mass ratio. Instructions are given to the readers so that the readers can pursue this enumeration technique for themselves.

The traditional classification of real numbers (R) as a complete ordered field is contested throughcritical examination of the field axioms, with a focus on the absence of a multiplicative inverse for zero. We propose an alternative mathematical structure based on Energy Numbers (E), deriving from quantum mechanics, which addresses the classical anomalies and fulfills field properties universally, including an element structurally analogous but functionally distinctive from the zero in R.

A 3-manifold geometry offers an alternative theory for baryon rest mass splitting. A number of formulae are given that approximate a selection of lighter baryons within a few standard deviations of observation. The extreme density this theory necessitates is not compatible with the quark model.

It is thought that consideration of the General Relativity force law demonstrates that particles will retain their stationary status in the standard cosmological models. However this argument neglects the effects of pressure-dependent gravitational forces. When these forces are correctly included, what actually happens is that in spatially non-flat universes particles do not really remain co-moving, and indeed develop motion that is not consistent with the very symmetry condition these models were designed to manifest.

We examine, in general, the energy loss of electrons caused by the multiple Compton scattering of electrons on black body photons in the storage rings. We derive the scattering rate of electrons in the Planckian photon sea and then the energy loss of electrons per unit length. We discuss the possible generalization of our method in particle physics and consider a possible application of our formulas in case of motion of charged particles in the relic cosmological radiation.

Investigating conformal metrics on (Pseudo-)Riemannian spaces in any number of dimensions, it is shown that the pure scalar curvature R as the Lagrange densityleads to a homogeneous d'Alembert equation on spacetime which allows for source-free wave phenomena. This suggests to use the scalar curvature R itself rather than the Hilbert-Einstein action R*sqrt(abs(g)) as the governing Lagrange density for General Relativity to also find general, non-conformal solutions.

We study Dictionary of Ayurveda by Dr. Ravindra Sharma belonging to the Green Foundation, Dehradun, India. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BW(c=0.01),the magnetisation curve of the Ising Model in the Bragg-Williams approximation in the presence of external magnetic field, H. $c=frac{ H}{gamma epsilon}=0.01$ with $epsilon$ being the strength of coupling between two neighbouring spins in the Ising Model, $gamma$ representing the number of nearest neighbours of a spin, which is very large.

This paper investigates FinFET transistor technology, aiming to address limitations in conventional planar CMOS transistors. The motivation stems from the escalating demandfor high-performance, low-power devices in sub-10nm technology nodes. The challenges of short-channel effects, leakage currents,and scalability constraints in planar CMOS transistors have prompted exploration into novel architectures like FinFETs. This research provides an indepth analysis of FinFETs’ threedimensional structure, fabrication, materials, and design considerations. We evaluate their advantages and limitations compared to traditional transistors in terms of power consumption, speed, and scalability. Our approach involves comparative studiesutilizing simulations, material analysis, and empirical data. By merging theory with practical insights, this paper aims to offera comprehensive view of FinFET technology’s potential and challenges in modern semiconductor applications. In conclusion,this study sheds light on FinFET transistors, emphasizing their fabrication, design, and performance characteristics. It highlightstheir promise as a solution to semiconductor industry challenges, paving the way for next-generation electronic devices.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the founda-tion of such an approach is given. In part 2 it was shown how particle physics follows. Inthis 3rd part gravitational physics will be derived. In part 4 open fundamental questionsof actual physics are answered and the concept of a new cosmology is introduced.

We considered Weinberg-like equations in the article [1] in order to construct the Feynman-Dyson propagator for the spin-1 particles. An analog of the $S=1/2$ Feynman-Dyson propagator is presented in the framework of the $S=1$ Weinberg's theory. The basis for This construction is based on the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations. Next, We also analyzed the recent controversy in the definitions of the Feynman-Dyson propagator for the field operator containing the $S=1/2$ self/anti-self charge conjugate states in the papers by D. Ahluwalia et al~cite{Ahlu-PR} and by W. Rodrigues Jr. et al~cite{Rodrigues-PR,Rodrigues-IJTP}. The solution to this mathematical controversy is obvious. I proposed the necessary doubling of the Fock Space (as in the Barut and Ziino works), thus extending the corresponding Clifford Algebra. However, the logical interrelations of different mathematical foundations with physical interpretations are not so obvious. In this work we present some insights with respect to this for spin 1/2 and 1. Meanwhile, the N. Debergh et al article considered our old ideas of doubling the Dirac equation, and other forms of T- and PT-conjugation [5]. Both algebraic equation $Det (hat p - m) =0$ and $Det (hat p + m) =0$ for $u-$ and $v-$ 4-spinors have solutions with $p_0= pm E_p =pm sqrt{{bf p}^2 +m^2}$. The same is true for higher-spin equations (or they may even have more complicated dispersion relations). Meanwhile, every book considers the equality $p_0=E_p$ for both $u-$ and $v-$ spinors of the $(1/2,0)oplus (0,1/2))$ representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of negative-energy solutions. The recent Ziino works (and, independently, the articles of several other authors) show that The Fock space can be doubled on the quantum-field (QFT) level. We re-consider this possibility on the quantum-field level. In this article we give additional bases for the development of the correct theory of higher spin particles in QFT. It seems, that it is imposible to consider the relativistic quantum mechanics appropriately without negative energies, tachyons and appropriate forms of the discrete symmetries, and their actions on the corresponding physical states.

This paper introduces a preliminary concept aimed at achieving Artificial General Intelligence (AGI) by leveraging a novel approach rooted in two key aspects. Firstly, we present the General Intelligent Network(GIN) paradigm, which integrates information entropy principles with a generative network, reminiscent of Generative Adversarial Networks(GANs). Within the GIN network, original multimodal information is encoded as low information entropy hidden state representations (HPPs). These HPPs serve as efficient carriers of contextual information, enabling reverse parsing by contextually relevant generative networks to reconstruct observable information.Secondly, we propose a Generalized Machine Learning Operating System (GML System) to facilitate the seamless integration of the GINparadigm into the AGI framework. The GML system comprises three fundamental components: an Observable Processor (AOP) responsiblefor real-time processing of observable information, an HPP Storage Systemfor the efficient retention of low entropy hidden state representations, and a Multimodal Implicit Sensing/Execution Network designed to handle diverse sensory inputs and execute corresponding actions.

In this note, we present the Bursa-Wolf seven-parameter transformation from one geodetic system to another, showing how to determine the 7 parameters by the method of least squares and calculate them numerically following the number of the parameters 4,5 or 7.

Modern physics is no longer comprehensible to most people. This book explores the question of whether it is possible to develop a simpler and more intuitive physics. For this purpose, many ignored and overlooked physics relations are presented, which cannot be found in any textbook. These relations allow to develop a more holistic physics, which also builds a bridge to information theory and philosophy. Specifically, the book investigates, among other things, whether space consists of a structure of smallest elements, whether our universe is fractal, i.e. self-similar, whether we live in a black hole, what hidden commonalities there are in the fundamental forces, whether fundamental particles and hydrogen can be meaningfully described without quantum physics, whether black holes and fundamental particles are related, whether the formalism of special relativity really makes sense, whether particle spin can be explained classically, how gravity and quantum physics might be brought together and what the Sommerfeld constant is all about. To shed light on these questions, also parts of the works of Horst Thieme, Nassim Haramein, Dr. Randell Mills and Erik Verlinde are presented.

Runtime Application Security Protection (RASP) is crucial in safe-guarding applications against evolving cyber threats. This research presents a novel approach leveraging a fine-tuned BERT (Bidirectional Encoder Representations from Transformers) model as the cornerstone of a robust RASP solution. The fine-tuning process optimizes BERT’s natural language processing capabilities for application security, enabling nuanced threat detection and mitigation at runtime. The developedRASP system harnesses BERT’s contextual understanding to proactively identify and neutralize potential vulnerabilities and attacks within diverse application environments. Through comprehensive evaluation and experimentation, this study demonstrates the efficacy and adaptability of the BERT-based RASP solution in enhancing application security, thereby contributing to the advancement of proactive defense mechanisms against modern cyber threats.

This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed volume. We discuss then the basic applications of linear algebra to questions in analysis. Then we get into the study of the closed groups of unitary matrices $Gsubset U_N$, with some basic algebraic theory, and with a number of probability computations, in the finite group case. In the general case, where $Gsubset U_N$ is compact, we explain how the Weingarten integration formula works, and we present some basic $Ntoinfty$ applications.

This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:mathbb Rtomathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and of the integral $int_a^bf(x)dx$. Then we investigate the case of the complex functions $f:mathbb Ctomathbb C$, and notably the holomorphic functions, and harmonic functions. Then, we discuss the multivariable functions, $f:mathbb R^Ntomathbb R^M$ or $f:mathbb R^Ntomathbb C^M$ or $f:mathbb C^Ntomathbb C^M$, with general theory, integration results, maximization questions, and basic applications to physics.

The internal structure of the natural numbers reveals the relation between the weak and strong Goldbach's conjectures. Explicitly, if the weak Goldbach's conjecture is true, the strong Goldbach's conjecture is, and Goldbach's conjectures are true.

Goldbach’s numbers, all-natural integers which satisfy Goldbach’s conjectures are all odd integers and a subset of the even integers. Naturally, they appear in the proof of Goldbach’s conjectures. In this paper, the construction of Goldbach’s numbers approach is used to prove Goldbach’s conjectures, hopefully, it will bring a happy end.

In the context of computational methods, an experiment on the optical Fourier transform with direct phase measurement (Nature 2017) is analyzed, a correct assessment of its actual computational complexity is made, taking into account interference that exceeds the capabilities of computational methods, and an experiment technique for direct measurement of computational complexity is presented.<p>В контексте вычислительных методов разбирается эксперимент по оптическому преобразованию Фурье с прямым измерением фазы (Nature 2017), производится корректная оценка его действительной вычислительной сложности с учётом помех, превосходящей возможности вычислительных методов, приводится методика эксперимента по прямому измерению вычислительной сложности.

We propose the topological object, a gravitational knot, could exist in Newton's theory of gravitation by assuming that the Ricci curvature tensor especially the metric tensor consists of a scalar field i.e. a subset of the Ricci curvature tensor. The Chern-Simons action is interpreted as such a knot.

By assuming that the Ricci curvature tensor consists of a subset (scalar) field, we propose that Newton's second law of gravitation in (2+1)-dimensional space-time, a linear equation, could have hidden nonlinearity. This subset field satisfies a non-linear subset field theory where in the case of an empty space-time or the weak field, it reduces to Newton's linear theory of gravitation.

We will define a superset of integers (the complete integers), which contains the dual of integers along parity (e.g. the odd zero, the even one, ...). Then we will see how they form a ring and how they can be used as exponents for real numbers powers, in order to write functions which have a discontinuity in zero (the function itself or one of its derivates), as for example |x| and sgn(x).

We use the strichartz estimate and commutator estimates to prove the decay property of the solution. The global results can be obtained by the decay property.

Exploring n! + 1 = m^2 for natural number solutions beyond n = 4, 5, 7 confirms no further solutions exist,validated by using GCD Linear Combination Theorem

This paper focuses on question difficulty estimation (calibration), and its applications in educational scenarios and beyond. The emphasis is on the use of Active Learning to bound the minimum number of labelled samples that we need. It also explores using various SOTA methods for predicting question difficulty, with a specific focus on German textual questions using the Lernnavi dataset. The study refines preprocessing techniques for question data and metadata to improve question difficulty estimation.

STNs are highly efficient in warping the input image for a downstream task. However, cascaded STNs are found to be able to learn more complex transformations. We attempt to leverage the multistep process of diffusion models to produce module(s) that has a similar effectto cascaded STNs.

This work presents a modified Born-Infeld field theory and a numerical solution procedure to compute electron-like solutions of this field theory in the form of rotating waves of finite self-energy. For the well-known constants of real electrons, the computed solution results in a Born-Infeld parameter of 5x10^22 V/m, which is consistent with previous work.

This is a rendition of [2]. We study stringy motivic structures. This builds upon work dealing with $mathbb{F}_p$-modives for a suitable prime p. In our case, we let p be a long exact sequence spanning a path in a pre-geometric space. We superize a nerve from our previous study.

This paper investigates the Diophantine equation pr + (p + 1)s = z2 Where p > 3, s ≥ 3 , z is an even integer. The focus of the study is to establish rigorous results concerning the existence of solutions within this specific parameter space. The main result presented in this paper demonstrates the absence of solutions under the stated conditions. The proof employs mathematical techniques to systematically address the case when the prime p exceeds 3, and the exponent s is equal to or greater than2, while requiring the solution to conform to the constraint of an even z. This work contributes to the understanding of the solvability of the given Diophantine equation and provides valuable insights into the interplay between prime powers and the resulting solutions.

To celebrate the launch of the "Tunisian Land Information System (TLIS)" project, we would like to recall some of the history of Tunisian geodesy since its inception, and describe in detail the terrestrial and spatial geodetic systems that have been used since then.

Since the key to artificial general intelligence (AGI) is commonly believed to be commonsense reasoning (CSR) or, roughly equivalently, discovery of a knowledge representation method (KRM) that is particularly suitable for CSR, the author developed a custom KRM for CSR. This novel KRM called Tumbug was designed to be pictorial in nature because there exists increasing evidence that the human brain uses some pictorial type of KRM, and no well-known prior research in AGI has researched this KRM possibility. Tumbug is somewhat similar to Roger Schank's Conceptual Dependency (CD) theory, but Tumbug is pictorial and uses about 30 components based on fundamental concepts from the sciences and human life, in contrast to CD theory, which is textual and uses about 17 components (= 6 Primitive Conceptual Categories + 11 Primitive Acts) based mainly on human-oriented activities. All the Building Blocks of Tumbug were found to generalize to only five Basic Building Blocks that exactly correspond to the three components {O, A, V} of traditional Object-Attribute-Value representation plus two new components {C, S}, which are Change and System. Collectively this set of five components, called "SCOVA," seems to be a universal foundation for all knowledge representation.

This 2023 document is a wrapper that embeds the author's original 2022 article of the above title that has never been publicly available before. The embedded article is about Phase 1 (which is about Tumbug) and Phase 2 (which is about non-spatial reasoning) of the 5-phase Visualizer Project of the author, a project that is still in progress as of late 2023. The embedded article is currently being re-released by the author to supply more information about that project to the public, and for historical reasons. The embedded article was written before a much more thorough article about Phase 1 (viz., "Tumbug: A pictorial, universal knowledge representation method") became available in 2023, but the embedded article describes results from Phase 2 that have not yet been documented elsewhere.

Fundamental results of special relativity, such as the linear transformation for Lorentz boosts, and the invariance of the spacetime interval, are derived from a system of differential equations. The method so used dispenses with the need to make any physical assumption about the nature of spacetime.

Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove that if $2^n-1$ has carries of degree at most $$kappa(2^n-1)=frac{1}{2(1+c)}lfloor frac{log n}{log 2}floor-1$$ for $c>0$ fixed, then the inequality $$iota(2^n-1)leq n-1+(1+frac{1}{1+c})lfloorfrac{log n}{log 2}floor$$ holds for all $nin mathbb{N}$ with $ngeq 4$, where $iota(cdot)$ denotes the length of the shortest addition chain producing $cdot$. In general, we show that all numbers of the form $2^n-1$ with carries of degree $$kappa(2^n-1):=(frac{1}{1+f(n)})lfloor frac{log n}{log 2}floor-1$$ with $f(n)=o(log n)$ and $f(n)longrightarrow infty$ as $nlongrightarrow infty$ for $ngeq 4$ then the inequality $$iota(2^n-1)leq n-1+(1+frac{2}{1+f(n)})lfloorfrac{log n}{log 2}floor$$ holds.

In this article, we characterize monomials in de facto values.Carlitz-Goss rielle defined on the complement of Fq (T) in a finite place which arealgebraic on Fq (T ). In particular, this confirms Wen-Yao's conjecturestated in 2003. This gives a necessary and sufficient condition on an en-p-adic tier so that the value of the Carlitz-Goss factorial in it is algebraic on Fq (T ). When restricted to rational arguments, we determinenot all algebraic relations between the values u200bu200btaken by this function, this which gives the counterpart for finite places of a result of Chang, Papanikolas, Thakur and Yu obtained in the case of infinite place.<p>Dans cette article, nous caractérisons les monômes en les valeurs de la facto-rielle de Carlitz-Goss définie sur le complété de Fq (T ) en une place finie qui sont algébriques sur Fq (T ). En particulier, cela confirme la conjecture de Wen-Yaoénoncée en 2003 . Celle-ci donne une condition necessaire et suffisante sur un en-tier p-adique pour que la valeur de la factorielle de Carlitz-Goss en celui-ci soit algébrique sur Fq (T ). Lorsque restreint aux arguments rationnels, nous détermi-nons toutes les relations algébriques entre les valeurs prises par cette fonction, cequi donne le pendant pour les places finies d’un résultat de Chang, Papanikolas, Thakur et Yu obtenu dans le cas de la place infinie.

In this note, we would like to show the simple results 1/0=0/0= tan(π/2)= cot(π/2)=0 based on the simple identities that are discovered by Keitaroh Uchida. The logic and results are all reasonable and exceptionally pleasant lookings for high school students.

Let $mathcal{O}subset mathbb{R}^d$ be a bounded domain of class $C^{1,1}$. In $ L_2(mathcal{O};mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $A_{D,varepsilon}$ with the Dirichlet boundary condition. Here $varepsilon >0$ is a small parameter. The coefficients of the operator $A_{D,varepsilon}$ are periodic and depend on $mathbf{x}/varepsilon$. The principal terms of approximations for the operator cosine and sine functions are given in the $(H^2ightarrow L_2)$- and $(H^1ightarrow L_2)$-operator norms, respectively. The error estimates are of the precise order $O(varepsilon)$ for a fixed time. The results in operator terms are derived from the quantitative homogenization estimate for approximation of the solution of the initial-boundary value problem for the equation $(partial _t^2+A_{D,varepsilon})mathbf{u}_varepsilon =mathbf{F}$.

We consider strings from the perspective of stable motivic, homotopical QFT. Some predictions for the behavior of gauginos in both a Minkowski light cone and $5$-dimensional $mathcal{A}dmathcal{S}_5$-space are given. We show that there is a duality between working locking in a system of dendrites, and threshold edging at the periphery of a manifold.This work extends the work of [4] and [7] by providing a more mathematical interpretation of the realization of quasi-quanta in open topological dynamical systems. This interpretation incidentally involves the category of pure motives over $mathfrak{C}$, and projections of fiber spectra to the category of stable homotopies.

In Geometric Algebra, G(1,3,1) is a degenerate-metric geometric algebra being introduced in this paper as Space Time PGA [STPGA], based on 3D Homogeneous PGA G(3,0,1) [3DPGA] and 4D Conformal Spacetime CGA G(2,4,0) [CSTA]. In CSTA, there are flat (linear) geometric entities for hyperplane, plane, line, and point as inner product null space (IPNS) geometric entities and dual outer product null space (OPNS) geometric entities. The IPNS CSTA geometric entities are closely related, in form, to the STPGA plane-based geometric entities. Many other aspects of STPGA are borrowed and adapted from 3DPGA, including a new geometric entity dualization operation J_e that is an involution in STPGA. STPGA includes operations for spatial rotation, spacetime hyperbolic rotation (boost), and spacetime translation as versor operators. This short paper only introduces the basics of the STPGA algebra. Further details and applications may appear in a later extended paper or in other papers. This paper is intended as a quick and practical introduction to get started, including explicit forms for all entities and operations. Longer papers are cited for further details.

Based on the quaternion domain Fourier transform (QDFT)of 2016 and the quadratic-phase Fourier transform of 2018, we introduce the quadratic-phase quaternion domain Fourier transform (QPQDFT) and study some of its properties, like its representation in terms of the QDFT, linearity, Riemann-Lebesgue lemma, shift and modulation, scaling, inversion, Parseval type identity, Plancherel theorem, directional uncertainty principle, and the (direction-independent) uncertainty principle. The generalization thus achieved includes the special cases of QDFT, a quaternion domain (QD) fractional Fourier transform, and a QD linear canonical transform.

In this note, we present the Bursa-Wolf seven-parameter transformation from one geodetic system to another, showing how to determine the 7 parameters by the method of least squares and calculate them numerically.

Null geodesics of a spacetime are a key factor in determining dynamics of particles. In this paper, it is argued that, within the scope of validity of Cosmological Principle where FLRW model can be safely employed, expansion of the Universe causes the null geodesics to accelerate, providing us with a universal acceleration scale a_0=cH_0. Since acceleration of null rays of spacetime corresponds to null rays of velocity space, demanding the invariance of acceleration of light a_0 yields a new metric for the velocity space which introduces time as a dimension of the velocity space. Being part of the configuration space, modification of distance measurements in velocity space alters the Euler-Lagrange equation and from there the equation of motion, Newton's Second Law. It is then seen that the resulting modification eliminates the need for Dark matter in clusters of galaxies and yields MOND as an approximation.

We have previously proposed a quintic equation that is outside the available arguments of the solvable quintic equation . In this article, we give another quintic equation in Bring - Jerrard form and its root.

The authentication is the process of determining whether someone or something is, and there are many authentication methods for digital environment. The digital authentication is divided into three main categories, 'What you have', 'What you know', and 'Who you are'. Furthermore, there are multi-factor authentications using a combination of two or more of these. However, these methods are always exposed to the risk of forgery, tampering, and stealing. This paper proposes a novel authentication architecture that is suitable for Internet of Things (IoT) and Internet of Behaviors (IoB) environment. In the aspect of technology, the proposed architecture is token based authentication method. However, this architecture is continuous, mimics real analog world, and has the advantage of being immediately recognizable in counterfeiting.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the foundation of such an approach is given. Here in part 2 it will be shown how particle physics follows. In part 3 gravitational physics will be derived. In part 4 open fundamental questions of actual physics are answered and the concept of a new cosmology is introduced.

One of the possible explanations for entanglement is a sort of perverse holonomy which acts on sheaves whose germs are eigenvectors for a tuple of local variables. We take baby steps towards realizing this model by introducing an equivariant form of holonomy. As a test category, we take U(1)-bundles whose outbound fibrations are Koszul nerves of degree (p+q)=n.

In this paper, we present elementary proofs of Wilker-type inequalities involving trigonometric and hyperbolic functions. In addition, we propose some conjectures which extend and generalize the Wilker-type inequalities.

We generalize the Li-Yau inequality for second derivatives and we also establish Li-Yau type inequality for fourth derivatives. Our derivation relies on the representation formula for the heat equation.

The Operator axioms have produced complete operations with real operators. Numerical computations have been constructed for complete operations. The classic calculator could only execute 7 operator operations: + operator operation(addition), - operator operation(subtraction), $times$ operator operation(multiplication), $div$ operator operation(division), ^{} operator operation(exponentiation), $surd$ operator operation(root extraction), log operator operation(logarithm). In this paper, we invent a complete calculator as a software calculator to execute complete operations. The experiments on the complete calculator could directly prove such a corollary: Operator axioms are consistent.

Fine-tuning pre-trained language models like Bidirectional Encoder Representations from Transformers (BERT) has exhibited remarkable potential in various natural language processing tasks. In this study, we propose and investigate the fine-tuning of BERT specifically for the classification of HTTP payload representations within network traffic. Given BERT's adeptness at capturing semantic relationships among tokens, we aim to harness its capabilities for discerning normal and anomalous patterns within HTTP payloads. Leveraging transfer learning by fine-tuning BERT, our methodology involves training the model on a task-specific dataset to adapt its pre-trained knowledge to the intricacies of HTTP payload classification. We explore the process of fine-tuning BERT to learn nuanced representations of HTTP payloads and effectively distinguish between normal and anomalous traffic patterns. Our findings reveal the potential efficacy of fine-tuned BERT models in bolstering the accuracy and efficiency of anomaly detection mechanisms within network communications.

The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specifically solve Real polynomial functions.

Probability, as manifested through entropy, is presented in this study as one ofthe most fundamental components of physical reality. It is demonstrated that thequantization of probability allows for the introduction of the mass phenomenon.In simple terms, gaps in probability impose resistance to change in movement,which observers experience as inertial mass. The model presented in the paperbuilds on two probability fields that are allowed to interact. The resultant prob-ability distribution is quantized, producing discrete probability levels. Finally, aformula is developed that correlates the gaps in probability levels with physicalmass. The model allows for the estimation of quark masses. The masses of theproton and neutron are arrived at with an error of under 0.04%. The masses ofsigma baryons are calculated with an error between 0.2% and 0.05%. The Wboson mass is calculated with an error of under 0.5%. The model explains whyproton is stable while other baryons are not, and it gives an explanation of theorigins and nature of dark matter. Throughout the text, the article illustratesthat the approach required to describe the nature of mass is incompatible withthe mathematical framework needed to explain other physical phenomena.

On an absolute frame of reference, a Galois connection to a d-brane may be prescribed such that the data of the frame becomes locally presentable. We describe these connections briefly.

In this paper, we prove a joint generalization of Arslanov’s completenesscriterion and Visser’s ADN theorem for precomplete numberings. Then we considerthe properties of completeness and precompleteness of numberings in the context ofthe positivity property. We show that the completions of positive numberings are nottheir minimal covers and that the Turing completeness of any set A is equivalent to theexistence of a positive precomplete A-computable numbering of any infinite family withpositive A-computable numbering.

I define the notions of complex curvature and complex radius and prove that one of these complex numbers is exactly the inverse of the other.

This article analyses the conjecture that excess mortality is underestimated with the pandemic.I use the numbers from the CBS (Dutch Central Bureau for Statistics) as an example. As a baseline we take the expected mortality for 2021 and 2022 from 2019. I correct this expected mortality with the estimated number of people who died in earlier years than expected because of the pandemic. For 2021 this correction is 8K. The CBS expects the mortality to be almost equal to the estimate from 2019. Then the excess mortality increases from 16K (CBS) to 24K.I present the following idea to explain the difference. At the beginning of very year the numbers of people in year groups are usually adjusted by applying a historical determined percentage to the population at January first. Covid hits the weakest the hardest. This changes the distribution of the expected remaining life years in the year group. And thus the average expected remaining life years. Hence the percentage has to be adjusted. Then the expected mortality decreases and the excess mortality increases.The excess mortality within a year are people who for example died in April from covid but who would have died in October without the pandemic. With this number total excess mortality rises with 6K to 30K.Excess mortality is divided in covid and non-covid. De large increase in non-covid deaths is striking.The analysis supports the conjecture that excess mortality is underestimated.Note: The numbers in this article are for the Netherlands. For you own country use the appropriate numbers.

This article discusses the influence of a disturbance like covid on the calculation of life expectancy in year groups etcetera. Life expectancies in year-groups are usually adjusted in the beginning of the year based on the population in the beginning of the year. This is done with a percentage based on previous years. This percentage is a reflection of volume. With the pandemic the weak were hit heavily by covid. A consequence is that the distribution of life expectancy changes in the year groups. This increases the life expectancy and decreases the expected mortality in the year group. Then the calculation for the year groups has to be adjusted accordingly. In this article I give an example of such adjustment. One can accordingly adjust likewise statistics.

The paper studies Σ-0-n-computable families (n ⩾ 2) and their numberings. It is proved that any non-trivial Σ-0-n-computable family has a complete with respect to any of its elements Σ-0-n-computable non-principal numbering. It is established that if a Σ-0-n-computable family is not principal, then any of its Σ-0-n-computable numberings has a minimal cover.

The recently observed gravitational wave background is explained in terms of the quantum modification of the general relativity (Qmoger). Some UFO, FRB and supernova flares also can be explained in terms of Qmoger.

In Geometric Algebra, G(3,0,1) is a degenerate-metric algebra known as PGA, originally called Projective Geometric Algebra in prior literature. It includes within it a point-based algebra, plane-based algebra, and a dual quaternion geometric algebra (DQGA). In the point-based algebra of PGA, there are outer product null space (OPNS) geometric entities based on a 1-blade point entity, and the join (outer product) of two or three points forms a 2-blade line or 3-blade plane. In the plane-based algebra of PGA, there are commutator product null space (CPNS) geometric entities based on a 1-blade plane entity, and the meet (outer product) of two or three planes forms a 2-blade line or 3-blade point. The point-based OPNS entities are dual to the plane-based CPNS entities through a new geometric entity dualization operation J_e that is defined by careful observation of the entity duals in same orientation and collected in a table of basis-blade duals. The paper contributes the new operation J_e and its implementations using three different nondegenerate algebras {G(4),G(3,1),G(1,3)} as forms of Hodge star dualizations, which in geometric algebra are various products of entities with nondegenerate unit pseudoscalars, taking a grade k entity to its dual grade 4-k entity copied back into G(3,0,1). The paper contributes a detailed development of DQGA. DQGA represents and emulates the dual quaternion algebra (DQA) as a geometric algebra that is entirely within the even-grades subalgebra of PGA G(3,0,1). DQGA has a close relation to the plane-based CPNS PGA entities through identities, which allows to derive dual quaternion representations of points, lines, planes, and many operations on them (reflection, rotation, translation, intersection, projection), all within the dual quaternion algebra. In DQGA, all dual quaternion operations are implemented by using the larger PGA algebra. The DQGA standard operations include complex conjugate, quaternion conjugate, dual conjugate, and part operators (scalar, vector, tensor, unit, real, imaginary), and some new operations are defined for taking more parts (point, plane, line) and taking the real component of the imaginary part by using the new operation J_e. All DQGA entities and operations are derived in detail. It is possible to easily convert any point-based OPNS PGA entity to and from its dual plane-based CPNS PGA entity, and then also convert any CPNS PGA entity to and from its DQGA entity form, all without changing orientation of the entities. Thus, each of the three algebras within PGA can be taken advantage of for what it does best, made possible by the operation J_e and identities relating CPNS PGA to DQGA. PGA G(3,0,1) is then doubled into a Double PGA (DPGA) G(6,0,2) including a Double DQGA (DDQGA), which feature two closely related forms of a general quadric entity that can be rotated, translated, and intersected with planes and lines. The paper then concludes with final remarks.

Maxwell wrote that he wanted to "leaven" his Treatise on Electromagnetism with Quaternions. Maxwell died before doing this. Silberstein and Conway accomplished this partially.This presentation claims the Lorentz condition field is the gravitational potential. Resulting in a Gravitic-Electromagnetic unification.

Exploring the concept of the external world's existence has been a focal point within the domain of epistemological inquiry throughout the annals of philosophy. Numerous thinkers have grappled with the question of whether one can truly fathom the existence of the external world and, if so, how such comprehension can be attained. Among these intellectual explorers stands David Hume, who approaches our perceptions of the external world as deeply rooted in matters of belief. Hume critically examines the belief in the enduring and distinct presence of external entities, even when these entities escape active perception. This inquiry delves into the origins of the belief in an external world that persists independently of our cognitive processes and sensory experiences, probing the cognitive faculties responsible for shaping such convictions. Through this exploration, it is asserted that Hume's primary aim is to illuminate the epistemological significance embedded within such beliefs.

In the present article, we classically derive an analytic formula of the Remnant Mass of a Quasi-Binary Black Hole. The Quasi Black Hole concept comes from a Theory Of Everything we have developed few years ago.

As in spite to intense search at present apparently there is no approach leading to a theory including the standard model of particle physics and general relativity, it is discussed whether such a theory is possible at all. In the following is shown that a ToE is possible if the either/or condition of current unification theories for background-dependent or -independent is replaced by a both/and. In this part 1, the foundation of such a theory is presented. In the following parts 2 and 3 particle and gravitational physics are derived from this foundation and in part 4 fundamental open fundamental questions of actual physics are answered by a new interpretation of physical quantities and an outline of a new cosmology is given.

Certain preconceptions about the physical world inherited from antiquity as yet permeate our established theories of physics and cosmology. Tacitly prominent in this world view is the fact that humans evolved on a 5.97 x 10^24 kg ball of matter.One of the consequences is the "relativistic" point of view, according to which accelerometers may or may not be telling the truth, whether they fall (a = 0) or when they are "at rest" on a planet’s surface (a > 0). The result of an experiment proposed by Galileo in 1632, but not yet performed, would unequivocally prove whether this schizoid relationship with accelerometers rings true or not.An imaginary alien civilization (of Rotonians) evolved on a rotating world in which the truthfulness of accelerometers is never doubted. Adopting a Rotonian perspective leads to a model of gravity according to which the result of Galileo’s experiment dramatically conflicts with the predictions of both Newton and Einstein.The consequences of this new perspective bear on and invite a rethink of many facets of established theories of physics and cosmology. Herein we discover that the Rotonian perspective is consistent with what we actually KNOW about the physical world and -- depending on the result of Galileo’s experiment -- it opens the door to a much more coherent, contradiction-free world view, which spans all scales of size, mass, and time.

Failure of LIGO physicists to provide a spacetime diagram showing the simultaneous laser paths and gravitational waves propagating through their interferometer is argued to be fatal to the whole enterprise.After establishing the cogency of this argument, the seemingly "unhackable" multi-messenger event GRB170817A is similarly placed under suspicion. Claims to have detected the gravitational waves from a coalescing neutron star binary suffer the red flag of a prominent (and suspiciously placed) glitch which prevented the event from triggering a real time alert to the community.Altogether, we have many reasons to suspect that all the claims of having detected gravitational waves are false. LIGO is a hoax. Perhaps the most dramatic way to expose the charade would be to at last perform the simple gravity experiment proposed by Galileo in 1632. We predict a result that conflicts with both Newton’s and Einstein’s theories of gravity. If our prediction is confirmed, gravitational waves and much else about modern gravitational theory would be falsified.Even if the result of Galileo’s experiment supports Newton and Einstein, we are way overdue to find out directly from Nature, instead of pretending to know, based on faith in popular theories.

This paper is a continuation of [2]. Here, we discuss twisted branes, the free loop superspace, and, in particular, a deformation of the modal lightcone which allows us to model cobordisms of generically small, portable, locally closed systems.

Haug and Spavieri have recently presented a new exact solution to Einstein’s field equations. In this paper, we will explore how this new metric could potentially lead to a new model for the cosmos. In the Friedman model, the cosmological constant must be introduced ad-hoc in Einstein’s field equations or, alternatively, directly into the Friedmann equation. However, a similar constant automatically emerges in our cosmological model directly from Einstein’s original 1916 field equations, which initially did not include a cosmological constant. We will analyze this, and it appears that the cosmological constant is little more than an adjustment for the equivalence of the mass-energy of the gravitational field, which is not taken into account in other exact solutions but is addressed in the Haug and Spavieri solution. Our approach seems to indicate that the Hubble sphere can be rep- resented as a black hole, a possibility that has been suggested by multiple authors, but this is a quite different type of black-hole universe that seems to be more friendly than that of a Schwarzschild black-hole.

Clifford algebras are an active area of mathematical research with numerous applications in mathematical physics and computer graphics among many others.The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension. This is achieved by the translation of the classical Faddeev-LeVerrier-Souriau (FVS) algorithm for characteristic polynomial computation in the language of the Clifford algebra. The FVS algorithm is implemented using the Clifford package in the open-source Computer Algebra System Maxima.Symbolic and numerical examples in different Clifford algebras are presented.

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex, smooth boundary domain $Omega$ in Plane; Payne conjectured that any second Dirichlet eigenfunction of laplacian in any simply connected bounded domain in Plane can not have a closed nodal line.

In this note, we give a method to resolve the equation β(φ)=Y used in geodesy, where β(φ) is the length of the arc of the meridian of an ellipse or an ellipsoid from the equator to the point of geodetic latitude φ.

The purpose of this study is to entrench the Copernican principle into cosmology with regard to dark energy (DE). A dual-universe solution is proposed for both the scale and coincidence problems of DE which is simple and involves no `fine-tuning'. It is also, in principle, testable and falsifiable. The model enables computation of the total entropy of the universe contained within the horizon expressed holographically projected onto the area of the cosmic horizon in units of Planck area. We subsequently compute the Planck entropy, which takes an irreducibly simple form. A derivation of the relation $[{DE}]={sqrt{m_{pl}.H_0}}$ is provided and we further show that this relation is valid in all (local i.e. $H'_{tau}=H'_0$) observer frames. We prove that the vacuum energy is exactly zero in this dual universe model. Lastly we propose that our analysis implies that the MOND paradigm is due to gravitation interaction of the two universes and we compute the MOND acceleration scale $a_0$ and scale invariant ${cal.{A}}_0$ as a consequence of cosmology, completely independent of galaxy dynamics. Significantly, this allows us to bring the MOND paradigm into a cosmological model without modifying General Relativity.

In this paper, ER bridges are discussed as bordisms. We treat these bordisms as fibers, whose sections are holographically entangled to copies of $S^1$. Diffemorphisms of these fibers are discussed, as well as the implication of replacing $S^1$ with the supercircle, and the replacing its underlying algebra with a Lie superalgebra.

We will demonstrate that the vacuum catastrophe can be solved by utilizing Bekenstein- Hawking entropy and applying it to black hole type cosmology models, as well as to a large class of Rh = ct models. Additionally, we will examine a recent exact solution to Einstein’s field equation and explore how it may potentially resolve the vacuum catastrophe rooted in both steady-state universe and possibly growing black hole universe scenarios.

In this note a model is put forward whereby the proton has mass and charge shell radii in the ratio 1:1.68. The fine structure constant is proportional to the thickness of the shell. Two new formulae for calculating �� are introduced. Eq 5 and Eq 6 are the centrepiece of this note. These make use of the usual set of fundamental constants, including the proton / electron mass ratio. Eq 6 gives the same value for $alpha$ as standard formulae. However, it is suggested that in an optimal physics, this method with reasonable confidence, gives a slightly lower value for �� reliable to 12 decimal places, i.e., $0.007297352566$. Whether this is the actual fine structure constant depends on the veracity of the model and the accuracy of the proton /electron mass ratio.

In this article, it is demonstrated that if the zeta function does not have a sequence of zeros whose real part converges to 1, then it cannot have any zeros in the critical strip, showing that the Riemann Hypothesis is false.

We have constructed a pitch structure. In this paper, we define a binary relation on the set of steps, thus the set become a circle set. And we define the norm of a key transpose. To apply the norm, we define a scale function on the circle set. Hence we may construct the 2-pitch structure over the circle set.

Hypergraphs are generalization of graphs, which have several useful applications. Sunflower hypergraphs are interesting hypergraphs, which become linear in some cases. In this paper, we discuss the Siedel spectrum of these hypergraphs.

We generalize atlases for flat stacks over smooth bundles by constructing local-global bijections between modules of differing order. We demonstrate an adjunction between a special mixed module and a holonomy groupoid.

It is investigated whether for real argument s the (s−1)n+1 weighted Riemann zeta ζ(n)(s) limits s ↓ 1 do exist. Here, we will look into n = 0,1. The answer to the question could very well be that assuming existence to be true gives a confusing outcome. That may support the possibility of incompleteness in concrete mathematics.

This paper conducts a security analysis of the generalized k-out-of-m spacetime-constrained oblivious transfer protocol in the context of relativistic quantum cryptography. The introduction of this paper provides an overview of relativistic quantum cryptography and delves into the details of the spacetime-constrained oblivious transfer protocol. The subsequent sections of the paper focus on determining the successful probability of various cloning and measurement attacks. The majority of the analysis will be based on the simplest case when m = 3 and k=2.

Diophantine treatment of Kepler laws, the Holographic Principle and Arthur Haas's forgotten Principle of Coherence induce a steady-state cosmology down to the billionth precision, which explains the observation of "impossible galaxies", and predicts the isothermicity of the background radiation at temperature 2.725820456 Kelvin. The connections of parameters with those of the solar system impose the Solanthropic Principle: we are alone in the universe.

In this brief paper we relate the universal gravitational constant G and Coulomb’s constant k to the volumes of subatomic particles. We define a new characteristic of subatomic particles, quantum volume, which varies in an inverse proportion to the mass of the subatomic particle. As an immediate corollary, we propose an explanation to the Proton’s radius puzzle that reconciles the various seemingly contradictory results obtained, checking our postulates with a prediction of upper and lower bounds for the electron’s radius which is consistent with the current experimental bounds.

General Relativity describes the gravitational field using the geometrical line element of a given generic spacetime metric where do not exists a clear difference between space andtime.This generical form of the equations using tensor algebra is useful for differential geometry where we can handle the spacetime metric tensor in a way that keeps both space and time integrated in the same mathematical entity (the metric tensor). However there are situations in which we need to recover the difference between space and time.The 3 + 1 ADM formalism allows ourselves to separate from the generic equation of a given spacetime the 3 dimensions of space(hypersurfaces) andthe time dimension.

A real matrix may not be similar to a diagonal matrix or a Jordan canonical matrix in the real number field. However, it is valuable to discuss the quasi-diagonalization and quasi-Jordanization of matrices in the field of real numbers. Because the characteristic polynomial of a real matrix is a real coefficient polynomial, the complex eigenvalues and eigenvector chains occur in complex conjugate pairs. So we can re-select the base vectors to quasi-diagonalize it or quasi-Jordanize it into blocks whose dimensions are no larger than 2. In this paper, we prove these conclusions and give the method of finding transition matrix from the Jordan canonical form matrix to the quasi-diagonalized matrix.

In this paper we firstly use a new method--the invariance of space-time interval and some simple linear algebra knowledge to derive Lorentz transformations and four-dimensional vectors. Finally we discuss and prove how to define the force and the momentum in relativity which has not been discussed and proved in textbooks and scientific literature. The first three dimensions of a four-dimensional momentum are defined as momentum and the derivative of momentum with respect to time is defined as force. But there is a problem that the rationality of the definition of momentum is not discussed and proved. Force and momentum cannot be arbitrarily defined. Because if our senses are sensitive and sophisticated enough, only a correct definition can guarantee that when we accelerate an object with a constant force, the momentum will increase at a constant rate. It is not necessary to be discussed in classical mechanics, because in classical mechanics the force is proportional to the acceleration and the force comes before the momentum. But it is just the opposite that the momentum comes before the force in relativistic mechanics, so it's important to discuss and prove how to define the force and the momentum in relativity. In addition the fact that the same physical process does not depend on the space-time point means that the Lorentz transformations must be linear transformations, so we can derive Lorentz transformations and four-dimensional vectors by using the invariance of space-time interval and some simple linear algebra knowledge.

Prigogine’s 1978 concept of dissipative structures, drawing parallels with living systems, forms the basis for exploring life’sunique traits. However, these identified similarities prove insufficient in capturing the entirety of life. To address this gap, ourproposed modeling approach emphasizes the distinctive ability of living organisms to observe other systems—an attributeintricately tied to quantum mechanics’ "measurement" processes, as highlighted by Howard Pattee. This article introduces acomprehensive mathematical model centered on quantum dynamical dissipative systems, portraying living systems as entitiesdefined by their observational capacities within this framework. The exploration extends to the core dynamics of these systemsand the intricacies of biological cells, including the impact of membrane potentials on protein states. Within this theoreticalstructure, the model is expanded to multicellular living systems, revealing how cells observe quantum dynamical systemsthrough protein state changes influenced by membrane potentials. The conclusion acknowledges the current theoreticalstatus of the model, underscoring the crucial need for experimental validation, particularly regarding the superposition state ofmembrane proteins under the influence of an electric field.

In this paper, we propose a variable modeling for the electric charge of subatomic particles, postulating that the charge of some subatomic particle with charge is dependent on its relativistic speed, with the speed of light as the main inertial reference frame. This variable modeling provides a solid explanation of the quantization of electric charge, and opens a new path of research in quantum physics.

In this brief paper we study and bound Mertens function. The main breakthrough is the obtention of a Möbius-invertible formulation of Mertens function, which with some transformations and the application of a generalization of Möbius inversion formula, allows us to reach an asymptotic rate of growth of Mertens function that proves the Riemann Hypothesis.

Miniature crycoolers are small refrigerators that can reach cryogenic temperatures in the range of 60K to 150K. They have the capability of accumulating a small temperature drop into a large overall temperature reduction. The cooldown time estimation is becoming more and more as a design parameter, certainly in hands-on applications. The various complicated physical processes involved in crycooler operation make it hardly possible to explicitly simulate the temperature time response. The numerical methods for solving a typical crycooler suffer from numerical instability,time step restrictions and high computational costs, among others. Since the operation of crycoolers involve processes in range of 15Hz−120Hz, actually solving the crycooler transient response would require different software tools to support the design and analysis of physical processes such as heat transfer, fluid dynamic, electromagnetic and mechanical. These processes would also require an excessive amount of calculations, incurring time consuming and precision penalty. In thisarticle we try to bridge the gap between the explicit impractical approach to steady state based approach. A framework developed in Python for calculating the cooldown time profile of anycrycooler based on a steady state database, is introduced, while utilizing a semi-analytic approach under various operating conditions. The cooldown time performance can be explored at various target and ambient temperature conditions, and also the effects of an external load, material properties or thermal capacitance on the overall cooldown time response. Two case studies based on linear and rotary crycoolers developed at Ricor are used for verfication, with a good agreement between the simulated and measured values.

In this paper, we compute an approximate value of vacuum permittivity constant (epsilon naught), with an error of less that 5%, using ether vacuum dipoles concept (Dirac's sea). We start from first principles by defining a field equation that will give bounded states dipoles, described as stationnary waves, and an equation for their polarizability density, very close to the vacuum permittivity value.

This paper presents a novel approach for calculating the solution to n-CongruencyAlgebraist Topologies using intrafunctorial calculus equations. We use a com-bination of the Primal Solution to n-Congruency Algebraist Topologies and theinterpspace calculus equation to calculate the finite integral associated with thealgebraic equations and the corresponding solutions for n. We show how thelogical operator "not" can be used in conjunction with the interpspace calculusequation to both calculate the integral and to negate the algebraic statement.We also provide an example of how this approach can be used to solve a partic-ular form of the equations. The results discussed in this paper can be appliedto a variety of problems in the field of algebraic topology.This paper explored the use of interpspace calculus and logical operations to calculate the finite integral solutions associated with the n-Congruency Algebraic Topologies equation and the associated solutions for n. We then applied this combination of methods to study the dynamics of the sun's gravitational pull on the planets orbiting it. Additionally, we developed a mathematical formulation to calculate the stability of a wormhole solution. Finally, we used the interpspace calculus equation and logical operations to derive an equation for the stability of a wormhole solution. This paper provides a comprehensive approach for studying the mathematics of stable wormholes.